So, while the Patriots smiled (OK, Bill Belichick didn’t really smile) and talked about how happy they were with Sunday’s 23-16 victory over the Miami Dolphins at Sun Life Stadium, we fretted about a suddenly stagnant offense, poor pass protection, dropped balls, and the unacceptability of a one-score game against a rookie quarterback and an obviously inferior opponent.

“That wasn’t ugly, that was a great win,’’ said Tom Brady, after a day in which he was sacked four times (tying his season high), threw his first interception since Oct. 14, passed for a mere 238 yards (24 for 40), and compiled a passer rating of 74.8, just a shade higher than the immortal Ryan Tannehill (66.2).

The Patriots came into this game having scored 190 points in their previous four games, which hadn’t been done since 1950. They were working with nine days of rest. The Dolphins are like fellow division tomato cans, the Bills and the Jets. They throw up all over themselves at the mere sight of No. 12 and the Hoodie.

We expected the Patriots to dominate the Dolphins.

But they did not dominate. They merely won.

“The last three times we’ve been here in December, we’ve lost,’’ noted Brady. “It’s not supposed to be easy, and it wasn’t.’’

It looked like it was going to be easy when the Dolphins botched a snap on a punt attempt and gave the Patriots the football on the 12-yard line in the second minute of play. The Patriots converted quickly and led, 7-0, with 11:53 left in the first quarter.

But scoring was a struggle after that. New England’s offensive line is battered and depleted. Brady was hurried and hit. He missed on several throws and the drops made things worse. Reshad Jones intercepted Brady late in the first quarter, snapping a streak of 201 passes without a pick.

Wes Welker caught 12 passes, but he dropped one in the end zone. The Patriots were shut out in the third quarter. After the Patriots moved the ball to the 2-yard line early in the fourth, Brady was sacked twice and New England settled for a field goal. In six games prior to Sunday, Brady was sacked only three times. The Dolphins got him four times in four quarters.

“We didn’t necessarily convert as often as we’d like,’’ acknowledged Brady. “I wish they all would have been touchdowns, but we’ve got to execute better in order to do that.’’

The victory gave the Patriots nine division titles in 10 years, missing only in 2008 — the year Brady went on the shelf in the first half of the first game. It’s Brady’s 10th division crown as a starting quarterback, the most in NFL history (Joe Montana had nine). It also marked the 44th consecutive game in which Brady threw at least one touchdown pass. Hope he doesn’t slug Kris Humphries and jeopardize his streak.

The Patriots didn’t tape cellophane to their lockers and go all wild-card Red Sox on us, but there was some well-earned satisfaction in the winner’s room. Every player had a “AFC East Division Champion” blue hat and gray T-shirt at his locker. Nate Ebner and Danny Aiken were among the few who walked around wearing the caps.

Not Brady. It would mess up his ’do, and he knows there’s only one goal in New England.

“The season starts now,’’ said the quarterback. “This is when the best teams start to separate themselves. We’ve got to get better and better and better. We’re not looking ahead. I think we’re a long way from that.’’

The Patriots play the 11-1 Houston Texans at Gillette a week from Monday night. A victory would give the Patriots a great shot to get a No. 1 or 2 seed and a first-round bye in the playoffs.

It’s a realistic goal for New England. With 7 more points this season, the Patriots could be 12-0. The AFC East is a joke and recent performances by Houston and Baltimore have taught us that the conference is up for grabs. The Patriots look capable of running the table and earning a ticket to New Orleans.

Some of us believe the Patriots have the best shot of any team in the conference simply because nobody else has Tom Brady.

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